Clock bias prediction for low Earth orbit satellites with LSTM neural network: method and verification

• Published in: GPS solutions Vol. 29; no. 3; p. 92
• Main Authors: Zhang, Wei, Zhang, Keke, Li, Xingxing, Huang, Jiande, Wu, Jiaqi, Yuan, Yongqiang
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2025; Springer Nature B.V
• Subjects: Accuracy; Aerospace environments; Atmospheric Sciences; Automotive Engineering; Bias; Earth and Environmental Science; Earth orbits; Earth Sciences; Electrical Engineering; Experiments; Geophysics/Geodesy; GRACE (experiment); Low earth orbits; Neural networks; Orbit determination; Polynomials; Satellites; Space Exploration and Astronautics; Space Sciences (including Extraterrestrial Physics; Spectrum analysis; Trends; Low Earth orbit (LEO) satellite; Neural network model; Clock bias prediction; Long-short term memory (LSTM) model; New strategy
• ISSN: 1080-5370; 1521-1886
• DOI: 10.1007/s10291-025-01851-7

Clock bias of low Earth orbit (LEO) satellite describes the discrepancy between the onboard clock indication time and the reference time, which can usually reach up to microseconds to milliseconds. LEO clock bias can significantly affect the accuracy of LEO-based applications such as navigation augmentation and timing. Despite that LEO clock bias can be determined along with orbit parameters during the precise orbit determination, the prediction of LEO clock bias remains challenging because LEO spaceborne oscillator is usually subject to intrinsic instabilities and intense variations of space environment. In this study, we focus on realizing the prediction of LEO clock bias using the long-short term memory (LSTM) model, a typical neural network model. Datasets from two gravity recovery and climate experiment follow-on (GRACE-FO) satellites covering the period of 10 months in 2023 are collected for our experiments. Our results reveal that the pronounced long-term linear and quadratic trends in clock frequency might severely degrade the prediction performance of the LSTM model. We therefore propose a new strategy (NS) where the quadratic polynomial fitting is performed on the epoch-differenced clock bias to eliminate these trends and generate the fitting residuals for model training and testing. The effectiveness of the NS is demonstrated by the resulting accuracy improvement of more than 30% and 90% for GRACE-C and GRACE-D, respectively. Benefiting from the NS of the LSTM model, the prediction accuracy of clock bias can reach (0.106, 0.360, 0.931, 1.157, 1.500) ns for GRACE-C, and (0.197, 0.753, 1.550, 1.969, 3.381) ns for GRACE-D, under the prediction time of (10, 30, 60, 90, 120) min. Compared with the predicted clock bias derived from the traditional spectrum analysis (SA) model, a representative analytical model for clock bias prediction, the LSTM-based results present a superior accuracy with the maximum improvement of 79.0% and 63.2% for GRACE-C and GRACE-D, respectively.